Science (In Antiquity)

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SCIENCE (IN ANTIQUITY)

Though science is often used in a broader sense, it is here taken to mean the conscious search for regularities in nature. To describe the first instances of such activity is impossible. This article reviews certain aspects of the search that have been ancestral to Western culture; they took place in Egypt, Babylonia, the Greek cities, and the Roman Empire. For the sake of continuity of ideas, the physical sciences and biological sciences will be treated separately.

Physical Sciences

The oldest scientific activity that scholars are acquainted with is that of Egypt, whose people used a calendar established prior to 2500 b.c. However—apart, perhaps, from the admiration of Egyptian accomplishment expressed in the writings of Herodotus and other Greeks—there are no indications that native Egyptian science ever rose to any considerable level. Astronomical observation was used for timekeeping. It gave rise not only to the concept of the four cardinal directions but also to their accurate determination; the Great Pyramid of Khufu (or Cheops), built about 2500 b.c., had a base aligned on true north within less than one-tenth of a degree. This sort of activity, taken together with the engineering skill manifested in so many ways—most strikingly in the fabrication, transportation, and upending the giant obelisks—might seem like a beginning from which a growth of science must follow. In fact, it did not follow; surviving papyri show that medicine, after an auspicious start, developed hardly at all during the succeeding 1,000 years, and that when the late Egyptians learned astronomy, they learned it not from their ancestors but from the Chaldeans and the Greeks.

The Chaldeans. The Chaldeans, or Babylonians, were intellectual heirs of the Old Babylonians, whose clay tablets dating from 1800 to 1600 b.c. show a highly developed arithmetic far surpassing that of the Egyptians. For example, one Old Babylonian tablet evaluates √2 to within one part in a million. If the Old Babylonians had an astronomy, little or nothing is known of it. Political and social upheaval submerged them and their Semitic conquerors; after 1600 b.c., there are but few tablets from Babylonia until the Seleucid period, which began in 312 b.c. From the four centuries that followed there is a wealth of recovered tablets, of which many hundreds contain astronomical texts or tables.

Cuneiform tablets dealing with astronomy were first deciphered by J. Epping, who worked from texts laboriously transcribed from clay tablets in the British Museum by J. N. Strassmaier [Strassmaier and Epping, "Zur Entzifferung der Astronomischen Tafeln der Chaldäer," Stimmen aus Maria Laach 21 (1881) 277–92]; their initial work was followed by the significant contributions of F.X. Kugler. Many other tablets have been translated in more recent years, notably by O. Neugebauer and his coworkers.

Though the Seleucid period followed the conquest of Babylon by Alexander, its culture was Babylonian, not Greek; the astronomers continued the development begun by their predecessors. Unlike the Greek methods, which were based on geometrical models, the Chaldean astronomical techniques were essentially arithmetical. Nevertheless, they were highly successful.

Development of the Calendar. The Chaldean astronomical techniques can be discerned in broad outline by considering the Chaldean calendar, whose fundamental units were the day and the month. The month was the period between successive new moons; a new day began at sunset, and a new month began on the first day at whose beginning the moon's new crescent was visible. This system generated two important problems of an astronomical kind. One was that some months had 29 days, whereas others had 30; it was desirable to know in advance how many days a given month would have. The other major problem was that a 12-month year would not stay in step with the sun; rigid adherence to a 12-month year would mean that a given month would not correspond to any particular season.

At first the authorities solved the second problem simply by inserting a 13th month in any year in which they deemed it beneficial. By about 400 b.c. astronomical progress permitted the establishment of a fixed system of intercalation. A lunation, the time between new moons, averages 29.5306 days as presently calculated, whereas the time between vernal equinoxes is 365.242 days. The latter figure multiplied by 19 is 6,939.60 days, and the former one multiplied by 235 is 6,939.69 days. Therefore 19 (tropical) years comprise almost exactly 235 lunations; and if a lunar calendar is contrived so that seven years in every 19 contain 13 months, the calendar keeps in step with the seasons moderately well, since (7 × 13) + (12 × 12) = 235. The period of 6,940 days is known as the Metonic cycle, because the relation just described was recognized (not later than 432 b.c.) by Meton of Athens; it has long been the basis of the ecclesiastical calendar.

The other problem, the prediction of the length of a month, was more complex. The first appearance of the moon, after conjunction with the sun, depends on a number of factors: the time interval between conjunction and sunset; the rate of motion of the moon with respect to the sun, which may be as little as 10° per day, or as much as 14°; the angle between the sun's path (the ecliptic) and the horizon, which at Babylon varies from less than 34° to nearly 81°, depending on the time of year; the departure of the moon's path from the ecliptic. The Chaldean method of taking all these effects into account was to approximate each time-varying element by means of a periodic and linear zigzag function, calculating the situation from day to day by increments based on arithmetic progressions, and then to sum the functions. To the modern mind, the method resembles Fourier analysis, but the functions added are linear zigzags instead of sinusoids, and their periods need not be simply related to one another. Sometimes step-functions took the place of the zigzags.

Museums contain many tablets of lunar ephemerides; these are simply tables of numbers, in which for each day the zigzags are added to find the relative positions of sun and moon and to indicate the day on which these would be such that a new month should begin. Each row gives the linearly approximated values of the variables for that day. For one method there are 18 columns of variables. An interesting by-product is the indication of whether or not the moon is new (or full) when it is on the ecliptic. If it is, then an eclipse of the sun (or moon) is possible. Even as late as the birth of Our Lord, there is no indication that the Chaldeans could be sure whether an eclipse of the sun would be visible or not.

Locating the Planets. The same technique of finding periods and appropriate zigzag or step-function approximations, and from these forming arithmetical progressions for the relevant variables, was applied to the planets. The goal was to predict the dates of visibility and invisibility of the planets, and also the dates of the "stationary points" mentioned below. The first and last appearances occur near the horizon, where refraction is a source of error, and the stationary points are not sharply defined. The attribution of great accuracy to the Chaldean observers is therefore no longer taken seriously. There is a little evidence that the astronomers were priests and that their interest was in the casting of horoscopes for the guidance of the government. Nowhere do the known tablets hint at geometrical models or at what would now be called a physical theory of the planets. In 1900, when scientists were thoroughly habituated to thinking in terms of models, many of them would doubtless have questioned whether Chaldean astronomy deserved to be called science, since it employed no models. (Quite probably it had an oral tradition along with the tablets, and the content of that tradition can only be guessed at.) In a view to which many scientists now subscribe, however, a scientist's task is merely to make systematically correct predictions of observable phenomena; a model is not a necessity, and it may be a hindrance. By this standard, the astronomy of the Chaldean tablets, when stripped of its astrological associations, must be regarded not only as science, but even as science operating by an exceptionally clean method.

The School of Miletos. Science as presently understood was developed by the Greeks. The first of these people associated with science were citizens of Miletos, a highly prosperous city on the west coast of what is now Turkey. Thales, the oldest of these men, was a successful businessman, active in politics. In Greek literature, he was regarded as the first natural philosopher, or physicist. The writers credit him with many accomplishments: recognition of electrification and of magnetism, the broadening of geometrical facts learned in Egypt into general propositions about similar triangles, the prediction of an eclipse of the sun (presumably in 585 b.c.) as a result of his contacts with Babylonian learning, and a belief that the moon shines by reflected light. Anaximander (fl. 570 b.c.), a slightly younger Milesian, made a systematic study of the shadows cast by an upright post (a gnomon) and therefrom drew conclusions about the motion of the sun. He stated that man evolved, through animals, from fishes. For him, the world was cylindrical, like a stone in a column, and unsupported; he made a map of it. Anaximenes (6th century b.c.), also of Miletos, stated that the stars are like nails fixed in a vault that rotates around the earth, and that a rainbow is made by the reflection of the sun's rays from a dense cloud. He put forward, too, the concept of man as the microcosmic parallel of the great cosmos.

Along with many valid conclusions, of which some of those just quoted are representative, the Milesian philosophers reached many that are not valid. Present-day knowledge of their thought, and even of the thought of most Greek scientists who lived later, is pitifully fragmentary. Typically, all that is preserved of their writings is a few quotations written down by other writers, perhaps centuries later, in books that happened to survive. Even the dates when important men lived are often uncertain.

Thales (fl. 590 b.c.) is a shadowy figure, from whom no writing survives. Certainly the story about his prediction of an eclipse is implausible, because all the evidence indicates that even hundreds of years later the Chaldean astronomers could predict only when an eclipse of the sun might be visible. With respect to Anaximander a bit more is known, because he wrote a book that survived until after 150 b.c.

The details of attribution to particular persons are uncertain and not really important. What matters is that Ionians of this period—or very little later—sought to explain the world in material terms, without resort to myth. Though their writings are lost except for a few brief quotations, one can probably catch something of their rationalist spirit in the writings of Herodotus, an Ionian who lived only about a century later, the text of whose history is well preserved. His weighing of plausibility of the various explanations of the Nile flood (Herodotus 2.19–29) makes firm contact with the mind of a modern scientist, whose methodology is so much the same.

Pythagoras. A quite different line of development stems from Pythagoras (fl. 530 b.c.), later than Thales but equally lost in the shadows. The extant accounts of Pythagoras as a person were written by uncritical biographers after a.d. 200, but it is fairly certain that he existed, that he was born an Ionian on the island of Samos, and that he established some kind of a brotherhood at Croton in the south of Italy. Though ascribing any particular advance in thought to Pythagoras himself is so risky as to be unjustifiable, some early and insistent traditions about the Pythagoreans are worth repeating. They are said to have been interested in geometry and also in number theory. That they knew the Pythagorean theorem, relating the square of the hypotenuse of a triangle to the sum of the squares of the other two sides, is plausible, but it is no great credit to them; the Old Babylonians knew and used the relation more than a millennium earlier. The contrast between Greek mathematics and Babylonian mathematics is nicely illustrated by their respective findings about √2. The Babylonians calculated it with great accuracy; the Greeks—very likely the Pythagoreans— proved that it is irrational.

The Pythagoreans developed a notable cosmology. Its outlines can now be perceived but vaguely, because it is known only from documents written long afterward and because at various times certain members of the group modified the system. There may also be the handicap of a tradition of secrecy in the brotherhood. Almost certainly, the Pythagoreans (or some of them) believed the earth to be a sphere. To Philolaus (fl. 430 b.c.), who was one of them, is ascribed the teaching that the universe is spherical too, but that the earth is not at its center. At the center he placed a Central Fire, and he had the earth revolve around it, along with the moon, the sun, the other planets, and the sphere of fixed stars. The distances of these bodies from the Central Fire were different; they probably increased in the order just given.

The Pythagorean universe is distinguished by a counterearth (ἀντíχθων). For the introduction of this body, two motives are given by Aristotle. One of them (Cael. 293b 24) is that the counterearth can account for the fact that eclipses of the moon are more frequent than those of the sun. The other reason (Meta. 986a 12) was to bring the number of the celestial bodies up to ten, since that was a sacred number. The sphere of the fixed stars counted as one body, the counterearth and earth as two more; the sun, the moon, and five other planets raised the total to ten. The counterearth may have moved about the Central Fire on the opposite side of it from the earth and in an orbit of the same size, or it may have had a slightly smaller orbit and stayed between the Central Fire and the earth, thus shielding the antipodes from the fire.

The striking thing about this whole theory, of course, is that it ascribes motion to the earth and locates that body elsewhere than at the center of the universe. The earth traverses its orbit once every 24 hours, keeping its uninhabited or antipodal side toward the Central Fire. Its motion with respect to the sun causes day and night; the motion of the sun, in an orbit inclined to that of the earth, produces the seasons. Circular motions of the moon and the five remaining planets accounted for the major phenomena associated with these bodies. The inhabitants of Greece and neighboring countries had no direct view of the Central Fire, but the suggestion was made that the ashen light on the moon (now called earthshine and ascribed to sunlight reflected from the earth) was caused by rays from the Central Fire. To move in its orbit while keeping one side turned away from the fire, the earth would have to rotate, though this consideration is not mentioned in the accounts of the theory that have survived.

The importance attached to having ten bodies circling the Central Fire may seem bizarre now, but it illustrates perhaps the most characteristic trait of Pythagoreanism, which is an emphasis on number. Legend attributes to Pythagoras himself a discovery that two strings sounding one of the musical intervals (an octave, for example, or a fifth) have lengths in the ratio of small integers. Aristotle (Meta. 985b 23–986a 3) says that in part because of this discovery, the Pythagoreans supposed numbers to be the basis of all things and the heavens to be numerical and musical. The type of reasoning is exhibited in Plato's argument that the number of elements needed in the universe is four (Tim. 31B–32B). Though such arguments now seem like free flights of fancy, it is worth noting that the association of numbers with the musical intervals must have been based on experiment—or, at the very least, on quantitative observation of a real phenomenon.

Except perhaps for some of the Pythagoreans, the Greeks whose scientific opinions have been discussed thus far were all Ionians, from the coast of Asia Minor or the islands nearby. The last important representative of this tradition was Anaxagoras of Clazomenae (fl. 460 b.c.), and he was the first of them to take up residence in Athens, where he became a friend of Pericles. Of his writings there has been preserved an exceptionally large remnant—more than a dozen fragments, comprising in all about three pages of a modern book. From these one learns that he ascribed the brightness of the moon to light from the sun, and the rainbow to the reflection of sunlight by clouds. He believed in a plurality of worlds, the other worlds than the earth having their men, their animals and cultivated fields, and "a sun and a moon and the rest as with us." Later Greek commentators state that Anaxagoras considered the earth to be flat and the stars to pass under it; that he considered the sun to be a fiery stone larger than the Peloponnesos, and the moon to be closer than the sun and of the same material as the earth; also that he was the first to explain correctly the origin of the moon's light and the relations of sun, moon, and earth during eclipses. Though he may well have understood the origin of the moon's light and the nature of eclipses, it is not really likely that he was the first to do so. In 467 b.c. a sizable meteorite (the elder Pliny says it was the size of a wagonload) fell at Aegospotami, on the Gallipoli Peninsula; Anaxagoras maintained that it had fallen from the sun. Perhaps it was this event which caused him to assert that the sun is a hot stone and that the moon is earth-like. These views were too much for the Athenians, and Anaxagoras was tried for impiety in about 432. Perhaps the real motive for the trial was political and related to his friendship with Pericles. Whatever the motive, it is interesting that Anaxagoras's opinions on cosmology could be used as a reason or a pretext for driving him out of Athens.

The Nature of Matter. Along with their concern for cosmology, these Ionian philosophers pondered the nature of matter. The early ones all adopted a species of monism, a belief that there is just one ultimate substance. Thales thought it to be water. Water was the natural choice, since Thales knew it not only as the lifegiving liquid but also as rigid ice and aerial steam.

Later Ionians differed from Thales in their choice of the primordial material. His fellow citizen Anaximander concluded that no substance known to the senses will serve, so he postulated a fundamental stuff, which he called ἄπειρον, the "unlimited," or "indefinite." In the next generation Anaximenes of Miletos held that the primary substance is air; when rarefied, it is fire, whereas in successive states of compaction it is water, earth, and rock.

Parmenides (fl. 470 b.c.) gave Greek thought a new direction by insistence on rigor in reasoning. His logic led him to distinguish between the evidence of the senses and the dictates of reason. Reason, he argued, forbids the ascription of different forms to the One. Yet reason recommends monism, though the senses demand recognition of change, which implies pluralism.

The ideas of Parmenides were applied and enlarged by Empedocles (fl. 450 b.c.), who, however, accepted sense perception as a guide to inquiry. To explain the changes that matter undergoes, he posited the existence of four root substances (ῥιζώματα) and two agents of change, φιλότης and νε[symbol omitted]κος, commonly translated as Love and Strife but having physical manifestations corresponding approximately to attraction and repulsion. The four Empedoclean elements, fire, air, water, and earth, held an important place in European thought for the next 2,000 years. By observing the behavior of what amounted to an inverted funnel dipped into water while its upper orifice was alternately shut and open, Empedocles demonstrated that air is corporeal.

Probably influenced by the strictures of Parmenides, Anaxagoras offered a combination of monism and pluralism. His unitary and unmixed element was νο[symbol omitted]ς, for which the customary translation is Mind. It is the cause of motion, or change, in all things. All things were in the beginning thoroughly mixed, but under the action of whirls or vortices caused by νο[symbol omitted]ς, they have become partially separated, so that they are experienced in states approximating purity. Only νο[symbol omitted]ς is completely separated from any other entity; Anaxagoras wrote that "there is a portion of everything in everything," asking "How can hair be made of what is not hair, or flesh of what is not flesh?" He urged that what appears as "coming into being" or "passing away" is merely the mingling or separation of things that are, thus formulating (perhaps not for the first time) the principle that matter is conserved; however, he believed not in atoms but in the unlimited divisibility of matter, saying that what is cannot cease to be, by being cut.

Leucippus, probably of Miletos, took a different view, which was elaborated by his disciple Democritus of Abdera (fl. 420 b.c.). They introduced the concept of atom (ἄτομος, uncuttable) and coupled with it the concept of vacuum. The atoms were invisibly small, infinite in number, alike in substance but different in shape. The differences in things arose from differences in the shapes, positions, and arrangement of the atoms, which were in motion in the vacuum. Coming into being was the aggregation of atoms, and passing away was their dispersal; the atoms themselves were indestructible. The theory thus reconciled stability with endless change. Aristotle rejected this escape from monism, but it was adopted by Epicurus (fl. 301 b.c.) and his many followers, and was described at length in the didactic poem De rerum natura by Lucretius about 60 b.c. The atomic hypothesis became a part of the learned tradition and was a basis for the thought of Boyle, Newton, and others during the rebirth of science in the 17th century.

Though the foregoing paragraphs describe many hypotheses that have proved fruitful, the Greek record thus far was not one of continuous advance. A major reason is that the key to progress in science—heavy reliance on propositions that can be tested by interrogating Nature— had not yet been found. The next century, roughly 425 to 325 b.c., belongs to Socrates (fl. 430 b.c.), his pupil Plato (fl. 387 b.c.), and Aristotle (fl. 344 b.c.), pupil of Plato and tutor of Alexander the Great. It began with an upsurge of interest in moral, rather than natural, philosophy; but it ended with science reestablished on a new and far firmer base.

Early Planetary Systems. Though he belittled science, Socrates contributed to its improvement by his strictures on unsound reasoning. Plato's primary concern was with moral questions; however, he valued mathematics and fostered not only its development but also its application in science, particularly in astronomy and geography. One of the great mathematicians of all time, Eudoxus of Cnidos (fl. 368 b.c.) was associated briefly with Plato's Academy. Along with basic work in mathematics, Eudoxus accounted for the appearance of the stars and the planets by means of combinations of uniform circular motions. His universe consisted of 27 spheres homocentric (i.e., concentric) with the earth. The outermost sphere carried the fixed stars and rotated once per day, westerly. The innermost sphere carried the moon and rotated westerly with a period of 27 days; its axis was carried by a sphere that rotated easterly and made one revolution in 223 lunations, and this in turn was carried by a larger sphere that moved in the same way as that of the fixed stars. By assigning appropriate directions to the axes of these three motions, Eudoxus was able to account quite well for the rather complicated course of the moon's position, expressing it as the resultant of three uniform circular motions. Similarly, he assigned three spheres to move the sun, and four each to Mercury, Venus, Mars, Jupiter, and Saturn. The system did not account well for the motion of Venus, and for Mars it failed miserably, but it accounted well for the then-known appearances of the other bodies. The progression of ideas from Thales to Eudoxus took only two centuries.

The system of Eudoxus was a work of genius. It brought order to the seemingly irregular motions of the planets, and did so with great economy of means; present-day heliocentric theory employs six adjustable constants for each planet, but Eudoxus's earth-centered system used only three. More important, the theory could be tested by comparing it quantitatively with the world of experience, and its shortcomings could be alleviated by making better choices of the constants and by employing additional spheres when they were needed, as for Venus and Mars and for newly discovered details of the motions.

Eudoxus had the first recorded observatory in Greece. Very likely his theory stimulated observation, and certainly it was elaborated and better fitted to the data by his follower Callippus (fl. 330 b.c.). This establishment of an interplay between theory and observation is a momentous event—perhaps the major event—in the history of Greek astronomy.

Very soon after Eudoxus, Heracleides of Pontos (fl. 350 b.c.) made two stupendous proposals whose adoption would further simplify the scheme of the universe. The first was that what rotates in one day is not the heavens, but the earth. The second—based, almost certainly, on the fact that Mercury and Venus are seen always in directions close to that of the sun—was that these two planets revolve not around the earth, but around the sun. A few decades later Aristarchus of Samos (fl. 270 b.c.) went all the way and taught that only the moon circles the earth, which is a planet that circles the sun along with all the other planets—an anticipation of the Copernican hypothesis. The earth rotates, while the sun and the stars are at rest. In a treatise that has survived, Aristarchus deduced from observation that the diameter of the earth is about three times that of the moon, and that the sun is very much larger than the earth. He reached this conclusion when he was yet young, and very likely it was the basis of his heliocentric hypothesis, since to assume that a large body revolves around a smaller one is dynamically unattractive. The heliocentric hypothesis, though preserved in the literature, won few converts.

Aristotle. Aristotle transmitted to Christendom a qualitative and cumbersome adaptation of the system of Eudoxus. It was cumbersome because Aristotle, who did not believe in the existence of empty space, made the spheres into material bodies with no space between them, so that the movement of one influenced all the others. To compensate for the undesired motions thus induced, Aristotle had to introduce additional spheres rotating in reverse. Thus, instead of working with at most five coupled spheres, as Callippus did, the users of Aristotle's system had to work with 56. The change was ruinous. Though Greek astronomy passed Aristotle by, the scholarly world held to his books while it all but lost those of the working astronomers.

Denying the possibility of empty space, Aristotle had to reject atomism. He accepted the Empedoclean elements; but in order to provide for a continuum of properties and for the conversion of one element into another (e.g., when water by boiling changes into air), he associated with each element two qualities from the contraries hot and cold, fluid and dry. Thus, earth is dry and cold, air is hot and fluid, and so on. (Concerning the transformation of element into element, see Gen. et cor. bk. 2.) These elements move naturally in straight lines—earth and water toward the center of the universe, but air and fire away from the center. To the unchanging heavens and their natural circular motion, Aristotle assigned a fifth and unchanging element, the ether.

Aristotle's physics is notorious. How could such a great genius go so far wrong? The popular idea that he disregarded experience is merely folklore; in Aristotle's scientific treatises, appeals to observed phenomena are frequent. It has been suggested that the physical treatises were composed early, while Aristotle was still under the Pythagorean influence of Plato, and that the biological treatises, which are brilliant in their observations and insights, were composed in later years, when Aristotle had learned to do valid research. An objection to this view is that the treatises were used by Aristotle in his teaching at Athens near the end of his life and that presumably they, like any other teacher's lecture notes, would be revised as his thinking changed. Perhaps the fact is that Aristotle thought in terms of form and function and that such analysis has been successful in biology but not in physics, where progress has come from mathematical analysis of idealized "models." However this may be, what actually put Aristotelian physics into bad repute was the parroting of it by the schoolmen of Europe nearly 2,000 years after he died. He should not be blamed for their failure, since their method was very non-Aristotelian.

The Alexandrian School. The golden age of Greek science occurred during the Hellenistic period, which began nearly coincidentally with the death of Aristotle. Its center was not Athens but Alexandria, where the Museum, with its great library, played much of the role of a modern university. Of the giants in mathematics and the physical sciences who did some of their work there, this article can mention only a few: Euclid (fl. 300 b.c.), Archimedes (fl. 247 b.c.), Eratosthenes (fl. 235 b.c.), Hipparchus of Nicaea (fl. 150 b.c.), and ptolemy (fl. a.d.150).

Euclid, in his Elements (στοιχε[symbol omitted]α), systematized the geometry of his time so admirably that no improvement was made in the next 2,000 years. G. Sarton has said that "Euclid created a monument that is as marvelous in its symmetry, inner beauty and clearness as the Parthenon, but incomparably more complex and more durable." It deals not only with what is now considered geometry but also with the theory of numbers. He also wrote on optics. Archimedes, who worked mainly in Syracuse, was also primarily a mathematician—an even greater one than Euclid, and one of the greatest of all time. Among his accomplishments were calculations of the volumes and surface areas of solids with curved surfaces, tasks now performed by means of integral calculus. In mechanics, he established statics and hydrostatics as mathematical sciences, quite unlike Aristotelian physics; he also won lasting fame as an inventor of actual devices. Eratosthenes is remembered chiefly for his work in geodesy. The Pythagorean belief that the earth is a sphere had been adopted by Plato and Eudoxus and endorsed by Aristotle, who not only cites several observations that support it but gives an estimate of its size, correct in general order of magnitude (Cael. 297a 9–298a 20). Eratosthenes, by means of the noon shadows of vertical posts, measured the difference in latitude between two points, Aswan and Alexandria, nearly on the same meridian and a known distance (about 500 statute miles) apart. His result was 252,000 stades; the length of his stade is uncertain, but a statement by Pliny (Naturalis Historia 12.53) leads to the inference that Eratosthenes's stade was 600 Egyptian cubits, so that his value for the polar circumference of the earth was 24,700 miles, in quite good accord with the modern value, 24,818 miles. It is fashionable to ascribe this accuracy to mere luck; but since his method has come down only in a secondhand and perhaps oversimplified account, composed several centuries later, the judgment may be too harsh.

Late Planetary Systems. Hipparchus, too, worked on mathematical geography, but he is rememberd chiefly as one of the truly great astronomers. None of his own major treatises has survived; his work is known mainly through the writings of Ptolemy, and the contributions made by Hipparchus cannot be known with certainty. However, it is generally agreed that he discovered the precession of the equinoxes, estimated well the distance and size of the moon, underestimated the distance and size of the sun (by about a factor ten), made a catalogue of the positions and magnitudes of some 850 stars, and brought to a state of high development the description of the planetary motions. Though his elder contemporary Seleucus the Babylonian had accepted the heliocentric model put forward by Aristarchus, Hipparchus was a principal contributor to the system that came to be called Ptolemaic. By this time Greek and Chaldean astronomy had come into close contact. The extent to which Hipparchus was influenced by Chaldean methods is uncertain, but it seems that at the very least he profited from the long records of observations that were kept in Babylonia.

Even though he knew that the sun is much larger than the earth, the rejection of the Aristarchian system by Hipparchus is not surprising. All other considerations apart, the Aristarchian system did not agree with the phenomena of the skies, since it employed circular orbits where elliptical ones meet the facts. Consider, for example, the apparent motion of the sun along the ecliptic. If the earth moved about the sun in a circular orbit, the sun would seem to move from vernal equinox to autumnal equinox in just half of 365¼ days, which is a little less than 183 days, and it would continue along to the vernal equinox in a like period. Actually, passage from the vernal equinox to the autumnal one takes 186½ days, and return to the vernal equinox occurs in the remaining 178¾ days. An earth-centered astronomy can account for this difference by assuming that the sun travels at a steady rate along a circle whose center is displaced from the center of the universe, the earth. Such an orbit is called an eccentric.

The apparent motions of the planets are more complex. Although their general tendency is to move eastward, as the sun does, with respect to the fixed stars, the planets sometimes move westward. To account for the retrograde motions, the Hellenistic astronomers developed the theory of epicycles. The planet moves uniformly around the epicycle, of which the center moves around the deferent circle. If the deferent is centered at the earth and if the center of the epicycle moves uniformly around it, then the resulting motion of the planet with respect to the earth is exactly equivalent to what would result if the earth and the planet moved around the sun in circular orbits, the orbits being in a single plane. Since the orbits with respect to the sun are in truth not circles and do not lie in a common plane, the deferent and epicycle just described cannot represent any planet's motion exactly; but they do take into account the gross aspects of a planet's motion as viewed from the earth.

It has well been remarked that the importance of a scientific treatise can be gauged by the number of earlier works that it renders superfluous. By this measure, two treatises that rank supremely high are Euclid's Elements and Ptolemy's Almagest (ἡμαθηματικὴσύνταξις); in their respective fields, both books supplanted the earlier treatises so completely as nearly to wipe out the evidence on which a history might now be based. Ptolemy left the planetary theory in highly developed form, in which the epicyclic principle is elaborated in a number of ways that permit better adjustment of the theory to the observed data. For example, he lets the deferent be not centered on the earth (i.e., it is an eccentric), and he lets the center of the epicycle revolve uniformly with respect to a point (the equant point) that is not even at the center of the deferent. This is a far cry from uniform circular motion around the earth. However, it seems certain that Ptolemy did not regard his system as a description of physical reality, but only as a computational analogue.

Ptolemy wrote also an influential and enduring treatise on geography, and one on astrology (the Tetrabiblos ) that bears his name is probably his. In the three centuries that separated Ptolemy from Hipparchus, progress in astronomy had been slow; after Ptolemy, it effectively ceased. By this time Egypt had been ruled directly by Rome for more than 100 years, and science was foreign to the Roman mind.

Philoponus. The last memorable Hellenistic contributor to science, john philoponus, worked in Alexandria as late as a.d. 525. Noteworthy parts of his voluminous output are his treatise on the plane astrolabe and his prolix but vigorous commentaries on numerous works of Aristotle. Though his ideas on falling bodies were not free from error, they were much in advance of Aristotle's; Philoponus states, for example, that if one weight is several times as heavy as another, the two will fall through equal distances in nearly equal times. In his discussion of the motion of an arrow, he rejected the Aristotelian formulation and put forward—indistinctly, to be sure—the idea of inertia. He also rejected Aristotle's distinction between sublunar and celestial matter, arguing that terrestrial and heavenly matter are the same in kind and have the same physics. He based his case partly on the conflict between Aristotle's ideas and the observable world; for example, Aristotle's fifth element, whose natural motion was a circling centered on the earth as the center of the universe, was not consistent with the epicyclic theory or with the sensory evidence that the planets are not at unvarying distances from the earth. Philoponus's belief in the physical unity of heaven and earth was supported, or perhaps inspired, by his monotheism and his belief that all matter was created by God.

Philoponus was a Christian (a Monophysite and perhaps a convert), though adherence to the scientific tradition usually implied loyalty to Greek ideals and therefore to paganism. He was the last of the Hellenistic physicists. The end of the Museum had come a century earlier, in a.d. 415, with the murder of its learned head, Hypatia. However, the Museum and the associated library had both seen their best days before the rise of Christianity and indeed even before Christ was born. As the Greek society that supported it became submerged, science slowly disappeared. The death of Archimedes at the hands of a Roman solider in 212 b.c. was a starkly symbolic event.

It is hardly too strong a statement to say that Rome had no native science. There was some effort by Romans to learn about Greek science, but this was only a scholarly activity, resulting in mere compilations in Latin of Greek lore and opinion. The sources were, for the most part, encyclopedic treatments of science by Greek popularizers; rarely were they the works of the scientists themselves.

The Biological Sciences

The scientific study of living things undoubtedly commenced as the study of sick or injured man. Surviving Egyptian medical treatises date from at least as early as 1500 b.c., and they derive from works very much older. Disease was believed to be caused by an invasion of the body by a deity, an enemy, or a dead person. The appropriate remedy was likely to be a prayer to Isis or to nine other beneficent dieties. The medical papyri give the proper incantations for various ailments; nevertheless, they do describe medicines and their mode of application. At least in part, the goal of the medicines seems to have been to make things unpleasant for the alien spirit that was causing the illness. Excrements from a whole ark of animals, from the fly to the hippopotamus, played prominent roles. Other animal, vegetable, and mineral products were also recommended, however, and some of the prescriptions may have had some degree of efficacy as sources of vitamins or other helpful compounds. At any rate, the pharmacopoeia of the Egyptian medical papyri is hardly more startling than that of England 30 centuries later. In the papyri that deal with bone surgery, there is no resort to magic; the tone is so rational that it can fairly be called scientific, though it does not go beyond the empirical.

Hippocrates and Aristotle. In Greece the scientific approach to medicine developed at Cos, an island near the coast of Asia Minor. The dominant figure was hippocrates (fl. 420 b.c.). From the school, which endured for generations, there survives a considerable body of writing, the Hippocratic Corpus; it is pragmatic, rational, clinical, devoid of superstition. Hippocratic medicine centered its effort on assisting the body to restore itself to health.

In zoology the greatest of the Greeks was Aristotle, son of a physician. He was a patient and acute observer, with a strong interest in marine animals and in embryology. A few of the phenomena that he described were not rediscovered until the 19th century. He made a strong start on the classification of animals; on the basis of blood, he separated the vertebrates from the invertebrates; he noted the distinction between bony and cartilaginous fishes; he classed whales not with fishes but with men and horses. Taking a strongly teleological view of the world, he rejected the idea of evolution by random trial, which had been put forward by Empedocles.

Aristotle's successor as head of the school that he had founded (the Lyceum) was his pupil and colleague Theophrastus (fl. 330 b.c.), who wrote the earliest systematic account of botany that has survived—one that was not surpassed until the 16th century. In Alexandria, Herophilus (fl. 300 b.c.) greatly advanced the knowledge of human anatomy by dissection of cadavers, a procedure that was rarely practiced during classical antiquity. Tradition says that he examined the internal organs of living criminals condemned to death; in an age when scourging and crucifixion were standard practice, it is a wonder that this was not one more often. Herophilus made many anatomical discoveries; among them was the recognition of the nerves. Aristotle had taken intelligence to be associated with the heart, but Herophilus returned to the earlier view that the seat of intelligence is the brain. His younger contemporary Erasistratus (fl. 260 b.c.) also made advances in anatomy, though he is more celebrated as a physiologist. He too dissected cadavers and, perhaps, living men. He distinguished between motor and sensory nerves, and he inferred the existence of capillaries connecting the arteries with the veins. Though his physiology invoked the idea of atoms, it depended heavily on varieties of vapor, πνε[symbol omitted]μα (Latin pneuma ), that were supposed to permeate the organism. One kind was carried by the arteries and another by the nerves, while blood flowed through the veins. He thought disease to be caused chiefly by excess of blood. Nevertheless, he discouraged bloodletting, which physicians of that time used habitually; he preferred to reduce the supply of blood by attention to diet.

Galen. In medicine, progress at Alexandria slowed earlier than it did in the physical and mathematical sciences. However, the last great figure, Galen (fl. a.d. 170), was a contemporary of the astronomer Ptolemy. Like Ptolemy, Galen was at once a contributor to his science and a codifier of the work of his predecessors, and his work dominated its field for about 1,500 years.

Born in Pergamon, Galen studied in Asia Minor and at Alexandria. In a.d. 162 he went to Rome, where he was spectacularly successful, becoming physician to the Emperor, Marcus Aurelius. His clear and forceful writings reflect a high regard for the Hippocratic school, but he was himself an able investigator. For dissections he depended mostly—perhaps entirely—on animals, especially monkeys. He made advances in the description of the muscles and of the functions of the spinal cord. He showed by experiment that the arteries, during life, carry blood. However, he was not aware that the blood circulates; he thought rather that it was consumed in the tissues. Galen did not establish a school, and when he died in a.d. 199 progress in medicine as a rational science came to a halt that, in the Christian world, lasted for more than 1,000 years.

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